One danger is that all the cheap Chinese crap will be redirected at Europe. It does have to upside of cheaper goods for Europe overall, which is fine for everything we don't make and which is overall adding value. The risk is that we also get all cheap plastic junk, unless EU regulations can keep it out environmental concerns.
I suspect that trade policy is one of the core competences of the EU.
And countries arguing for particular tariff policies and getting cutouts is widespread EU past time.